For \(c/a = 1.644\)  [1]} and the A-type AFM propagation vector (0,0,\(\frac{1}{2}\) ) r.l.u. [2]}, the MDI tensor eigenvalues for the three Cartesian ordered-moment axes are \(\lambda _{[100]} = 5.515\,488\,367\,755\,699\) , \(\lambda _{[010]} = 5.515\,488\,367\,755\,807\) using high-precision calculations, and \(\lambda _{[001]} = -11.0386\) . The in-plane anisotropy energy \(\Delta E\)  per formula unit of EuMg\(_2\) Bi\(_2\)  is given by
\(\Delta E = -\epsilon (\lambda _{[100]}-\lambda _{[010]}),\) 
